Chapter 5, Problem 12C

Explanation of Solution

Efficient recursive method for element uniqueness problem:

The efficient recursive method for element uniqueness problem is achieved with the running time of $\text{O}\left({\text{n}}^{\text{2}}\right)$.

• In a method, two for loops are used in cascade form to achieve the running time of $\text{O}\left({\text{n}}^{\text{2}}\right)$.

Method for Efficient recursive Algorithm:

Create the method uniqueness() that accepts the input parameter as “a” and “n” to compute the array elements are unique are not by calling this method recursively.

//Define the uniqueness() method

public int uniqueness(int[] a, int n)

{

  //Loop executes until length of array

  for (int i= 0 ; i <= (n-1); i++)

  {

  //Loop executes until length of array

  for(int j=i+1;j<=(n-1);j++)

  {

/*Check whether the array of first element is not equal to array of next element